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Abstract:

A control arrangement for controlling a piston pump unit for liquid
chromatography, in particular high-performance liquid chromatography, is
described. The piston pump unit has at least two piston-cylinder units
which operate cyclically in a phase-offset manner and generate, at an
outlet port, a predetermined flow of a liquid medium to be delivered. A
system pressure is established at the outlet port, irrespective of an
associated fluid load resistance. The control arrangement is configured
to record the pressure in the cylinder volume of at least a first of the
at least two piston-cylinder units. During a measurement phase of the
compression phase of the first piston-cylinder unit or during a
measurement phase of the decompression phase of the first piston-cylinder
unit, the control arrangement stops the drive device for the first
piston-cylinder unit for a predetermined time period and in the process
records measurement data which characterize the time profile of the
pressure.

Claims:

1. A piston pump unit for liquid chromatography comprising: (a) at least
two piston-cylinder units configured to generate, at an outlet port, a
predetermined flow of a liquid medium at a system pressure, (b) a control
device configured to (i) control a drive device for the at least two
piston-cylinder units, (ii) compress the liquid medium in a first
cylinder of the at least two piston-cylinder units in a compression phase
from a starting pressure to the system pressure, (iii) decompress the
first cylinder of the at least two piston-cylinder units in a
decompression phase, (iv) record pressure values as a function of time in
a cylinder volume of at least a first of the at least two piston-cylinder
units during a measurement phase, (v) stop the drive device for the first
piston-cylinder unit for a predetermined time period during a measurement
phase of a compression phase of the first piston-cylinder unit or during
a measurement phase of the decompression phase of the first
piston-cylinder unit; (vi) determine a correction dependence to correct a
piston movement of at least one of the at least two piston-cylinder units
during a compensation phase based on the recorded pressure values as a
function of time, and (vii) control the at least one of the at least two
piston-cylinder units using the correction dependence during the
compensation phase.

2. The piston pump unit of claim 1, in which the at least two
piston-cylinder units are further configured to operate cyclically in a
phase-offset manner.

3. The piston pump unit of claim 1 further comprising: a pressure sensor
configured to measure the pressure values in the cylinder volume.

4. The piston pump unit of claim 1, in which the correction dependence is
further based on a compression coefficient, a pressure value and a time
value when the compressing or decompressing of the first cylinder is
stopped, and another time value at a start of the compensation phase.

5. The piston pump unit of claim 4, in which the compression coefficient
is a ratio of a change in pressure values to an associated travel
distance of a piston in the first cylinder of the at least two
piston-cylinder units.

6. The piston pump unit of claim 5, in which the control device is
further configured to (vii) calculate the compression coefficient using
an equation, the equation comprising: QC=Δs/ΔP, where
QC is the compression coefficient, and ΔP is the change in the
pressure values for the associated travel distance Δs of the piston
in the first cylinder of the at least two piston-cylinder units.

7. The piston pump unit of claim 6, in which the control device is
further configured to (viii) calculate the correction dependence using an
equation, the equation comprising: s corr ( t ) = - Q C
( P M - P e ) ( - t - t 3 τ - - t 5 -
t 3 τ ) , ##EQU00017## where scorr(t) is the
correction dependence, t is a time value, QC is the compression
coefficient, PM is a pressure at a time t3 in which the
measurement phase starts, t5 is a time in which the compensation
phase starts, and Pe and τ are both parameters.

8. The piston pump unit of claim 1, in which the control device is
further configured to calculate parameters Ped and τd of
the correction dependence, where the measurement phase occurs during
decompression phase, using an equation and the recorded pressure values
as a function of time, the equation comprising: P tmess ( t ) =
P MD + ( P eD - P MD ) ( 1 - - t - t 21 τ D
) ##EQU00018## where Pmess(t) is the recorded pressure values
as a function of time, t is a time value, PMD is a pressure at a
time t21 in which the measurement phase starts.

9. The piston pump unit of claim 8, in which the control device is
further configured to convert parameters Ped and τd of the
decompression phase to parameters Pe and τ of the correction
dependence.

10. The piston pump unit of claim 7, in which the control device is
further configured to calculate an effective time constant for the
parameter τ using an equation, the equation comprising: effective
time constant = τ ( 1 - k Fl Fl max )
##EQU00019## where FL is a current flow rate, Flmax is a maximum
flow rate, and k is a constant factor between 0 and 1; and to input the
calculated effective time constant into the correction dependence for the
parameter τ.

11. A piston pump unit for liquid chromatography comprising: (a) at least
two piston-cylinder units configured to generate, at an outlet port, a
predetermined flow of a liquid medium at a system pressure, (b) a control
device configured to (i) control a drive device for the at least two
piston-cylinder units, (ii) compress the liquid medium in a first
cylinder of the at least two piston-cylinder units in a compression phase
from a starting pressure to the system pressure, (iii) decompress the
first cylinder of the at least two piston-cylinder units in a
decompression phase, (iv) record piston positions or piston speeds as a
function of time in a cylinder volume of at least a first of the at least
two piston-cylinder units during a measurement phase, (v) maintain a
constant pressure in the cylinder volume of the first piston-cylinder
unit for a predetermined time period during a measurement phase of a
compression phase of the first piston-cylinder unit or during a
measurement phase of the decompression phase of the first piston-cylinder
unit; (vi) determine a correction dependence to correct a piston movement
of at least one of the at least two piston-cylinder units during a
compensation phase based on the recorded piston positions or the recorded
piston speeds as a function of time, and (vii) control the at least one
of the at least two piston-cylinder units using the correction dependence
during the compensation phase.

12. The piston pump unit of claim 11, in which the control device is
further configured to calculate parameters se and τ of the
correction dependence using an equation and the recorded piston positions
or the recorded piston speeds as a function of time, the equation
comprising: s mess ( t ) = ( s M - s e ) - t -
t 3 τ ##EQU00020## where Smess(t) is the recorded piston
positions as a function of time, t is a time value, sM is a position
of the piston at a time t3 in which the measurement phase starts.

13. The piston pump unit of claim 12, in which the control device is
further configured to calculate an effective time constant for the
parameter τ using an equation, the equation comprising: effective
time constant = τ ( 1 - k Fl Fl max )
##EQU00021## where FL is a current flow rate, Flmax is a maximum
flow rate, and k is a constant factor between 0 and 1, and to input the
calculated effective time constant into the correction dependence for the
parameter τ.

14. A method of pumping a liquid with a piston-pump unit for liquid
chromatography, the method comprising: decompressing a first cylinder of
at least two piston-cylinder units during a decompression phase, in which
a volume of the first cylinder increases; compressing the liquid in the
first cylinder of the at least two piston-cylinder units during a
compression phase, in which a pressure of the liquid changes from a
starting pressure to a system pressure; measuring pressure values in the
volume of the first cylinder as a function of time during a measurement
phase of either the compression phase or the decompression phase; during
the measurement phase, stopping the compressing or the decompressing of
the first cylinder for a predetermined time period; after the compression
phase, outputting the liquid at an outlet port at the system pressure
during a delivery phase by decreasing the volume of the first cylinder;
and correcting a movement of a piston in the first cylinder of the at
least two piston-cylinder units during a compensation phase of the
delivery phase based on the measured pressure values.

15. The method of claim 14 further comprising: determining a correction
dependence to correct the movement of the piston in the first cylinder of
the at least two piston-cylinder units, the correction dependence being
based on a compression coefficient, a pressure and a time value when the
compressing or decompressing of the first cylinder is stopped, and
another time value at a start of the compensation phase.

16. The method of claim 15, in which the compression coefficient includes
a ratio of a change in a pressure to an associated travel distance of the
piston in the first cylinder of the at least two piston-cylinder units.

17. The method of claim 16, in which the compression coefficient is
calculated using an equation, the equation comprising:
QC=Δs/ΔP, where QC is the compression coefficient,
and ΔP is the change in the pressure for the associated travel
distance Δs of the piston in the first cylinder of the at least two
piston-cylinder units.

18. The method of claim 17, in which the correction dependence is
calculated using an equation, the equation comprising: s corr ( t
) = - Q C ( P M - P e ) ( - t - t 3 τ
- - t 5 - t 3 τ ) , ##EQU00022## where
scorr(t) is the correction dependence, t is a time value, QC is
the compression coefficient, PM is a pressure at a time t3 in
which the measurement phase starts, t5 is a time in which the
compensation phase starts, and Pe and τ are both parameters.

19. The method of claim 18, in which the compressing of the liquid in the
first cylinder is stopped at the time t3 for the predetermined time
interval.

20. The method of claim 18 further comprising: calculating the parameters
Pe and τ using the measured pressure values as a function of
time and a method of least squares.

21. The method of claim 18 further comprising: calculating an effective
time constant for the parameter τ using an equation, the equation
comprising: effective time constant = τ ( 1 - k
Fl Fl max ) ##EQU00023## where FL is a current flow rate,
Flmax is a maximum flow rate, and k is a constant factor between 0
and 1; and inputting the calculated effective time constant into the
correction dependence for the parameter τ.

22. The method of claim 14, in which a control device controls the
movement of the piston in the first cylinder of the at least two
piston-cylinder units.

23. The method of claim 16 further comprising: supplying the compression
coefficient of the liquid to a control device, in which the control
device controls the movement of the piston in the first cylinder of the
at least two piston-cylinder units.

24. The method of claim 16 further comprising: where the measurement
phase occurs during decompression phase, calculating parameters Ped
and τd of the correction dependence using an equation and the
measured pressure values as a function of time, the equation comprising:
P tmess ( t ) = P MD + ( P eD - P MD ) ( 1 - -
t - t 21 τ D ) ##EQU00024## where Pmess(t) is the
measured pressure values as a function of time, t is a time value,
PMD is a pressure at a time t21 in which the measurement phase
starts.

25. The method of claim 24 further comprising: converting parameters
Ped and τd of the decompression phase to parameters Pe
and τ of the correction dependence.

26. The method of claim 25 further comprising: calculating an effective
time constant for the parameter τ using an equation, the equation
comprising: effective time constant = τ ( 1 - k
Fl Fl max ) ##EQU00025## where FL is a current flow rate,
Flmax is a maximum flow rate, and k is a constant factor between 0
and 1; and inputting the calculated effective time constant into the
correction dependence for the parameter τ.

27. A method of pumping a liquid with a piston-pump unit for liquid
chromatography, the method comprising: decompressing a first cylinder of
at least two piston-cylinder units during a decompression phase, in which
a volume of the first cylinder increases; compressing the liquid in the
first cylinder of the at least two piston-cylinder units during a
compression phase, in which a pressure of the liquid changes from a
starting pressure to a system pressure; during a measurement phase of
either the compression phase or the decompression phase, measuring piston
positions or piston speeds in the first cylinder as a function of time;
during the measurement phase, stopping the compressing or the
decompressing of the first cylinder, maintaining a constant pressure
value in the volume of the first cylinder for a predetermined time
period; after the compression phase, outputting the liquid at an outlet
port at the system pressure during a delivery phase by decreasing the
volume of the first cylinder; and correcting a movement of the piston in
the first cylinder of the at least two piston-cylinder units during a
compensation phase of the delivery phase based on the measured piston
positions or piston speeds in the first cylinder as a function of time.

28. The method of claim 27 further comprising, calculating parameters
se and τ of the correction dependence using an equation and the
measured piston positions in the first cylinder as a function of time,
the equation comprising: s mess ( t ) = ( s M - s e )
- t - t 3 τ ##EQU00026## where Smess(t) is the
measured piston positions in the first cylinder as a function of time, t
is a time value, sM is a piston position at a time t3 in which
the measurement phase starts.

29. The method of claim 28 further comprising: calculating an effective
time constant for the parameter τ using an equation, the equation
comprising: effective time constant = τ ( 1 - k
Fl Fl max ) ##EQU00027## where FL is a current flow rate,
Flmax is a maximum flow rate, and k is a constant factor between 0
and 1; and inputting the calculated effective time constant into the
correction dependence for the parameter τ.

Description:

FIELD OF THE INVENTION

[0001] The invention relates to a control arrangement for controlling a
piston pump unit for liquid chromatography, in particular
high-performance liquid chromatography.

BACKGROUND

[0002] High-performance liquid chromatography (HPLC) is used to separate
liquid samples into their constituent parts by means of a chromatography
column (known as a column in the following text). In this case, the
separation performance of the column depends inter alia on the length
thereof and on the particle size of the packing material. For separation
which is as good as possible, columns having a sufficient length and a
small particle size are required. Such columns have high flow resistance
and therefore require considerably higher pressures than conventional
columns for operation.

[0003] Furthermore, sufficiently rapid separation is desired in order to
allow a high sample throughput. This requires a high flowing speed in the
column, with the result that the counter-pressure of the column likewise
increases.

[0004] For these reasons, modern, efficient HPLC installations operate
with increasingly high pressures. While pressures under 100 bar were
usual in the early stages of HPLC, current HPLC pumps can sometimes
deliver pressures above 1000 bar. This trend is continuing and is causing
a requirement for HPLC pumps which can deliver pressures considerably
higher than 1000 bar.

[0005] A basic requirement of pumps for HPLC is that the flow rate, called
flow in the following text, has to be delivered as far as possible
without pulsing and in a reproducible manner. In the case of gradient
pumps, which are capable of mixing two or more different liquid media
(also known as solvents in the following text) in a ratio which is
settable in a defined manner, the mixing ratio also has to be maintained
in a precisely defined manner and may not have any undesired
fluctuations.

SUMMARY

[0006] In a first embodiment, the invention is based on the finding that,
by briefly stopping the piston during the compression phase and recording
the time profile of the pressure during this measurement phase, it is
possible to obtain information which can be used to determine a
correction dependence scorr for controlling the piston or pistons in
the delivery phase following the compression phase or in the compensation
phase (within the delivery phase), during which a temperature
equilibration between the medium and the pump head takes place. The
correction dependence is determined by the control device, using the
measurement data obtained, such that by superposing the normal time
profile of the piston movement, i.e. the piston movement for generating
the desired (constant) flow without taking into account the thermal
equilibration effects, with the correction dependence, the piston or
pistons of one or more of the piston-cylinder units, which are used to
deliver the medium during the compensation phase, is or are controlled
such that in the compensation phase drops in the flow or in the pressure
are compensated or at least drastically reduced.

[0007] In general, the correction dependence can be determined for each
(following) cycle of the piston pump unit, or only at particular time
intervals or following triggering events, for example a change in the
composition of the medium to be delivered.

[0008] According to embodiments that are easy to realize, the control
arrangement determines the correction dependence scorr(t) such that
the flow fluctuations caused by the compressibility of the medium or the
flow fluctuations caused by the non-isothermal or adiabatic compression
and the associated thermal equilibration processes are compensated by an
addition of the correction dependence scorr(t) and the piston
movement of the at least one of the at least two piston-cylinder units,
which piston movement would bring about the desired flow without taking
into account the compressibility of the medium.

[0009] Advantageously, in order to determine the correction dependence
scorr(t), the control arrangement can use a predetermined,
preferably analytical theoretical dependence Ptheor(t) for the time
profile of the pressure and can determine one or more parameters of this
dependence using the measurement data recorded during the measurement
phase, such that the desired compensation effect, which is as optimal as
possible, is achieved. The theoretical dependence Ptheor(t) can be
stored in the control device as a functional analytical dependence or as
a profile (which is, for example, standardized and can be influenced by
one or more parameters) in the form of a table of values. The same also
applies, of course, to the actual correction dependence scorr(t),
the basic form of which does not have to be determined anew each time by
the control device using the theoretical dependence (and optionally
further constants or fixed temporal dependences). Rather, the control
device is generally configured such that it determines merely the
parameters of the correction dependence scorr(t).

[0010] Further improved accuracy can be achieved in that, during the
determination of the correction dependence scorr(t), the control
device takes into account the thermal equilibration occurring in the time
period from the start of the measurement phase to the start of the
compensation phase.

[0011] To this end, the control device can determine the correction
dependence scorr(t) for the piston movement s(t) using the
relationship

scorr(t)=scorr--theor(t)-scorr--theor-
(t5),

wherein t5 denotes the time at which the compensation phase starts,
and wherein the correction movement, necessary theoretically for
compensating the thermal effect, of the work piston
scorr--theor(t) is determined using the relationship

scorr--theor(t)=-QCΔPtheor(t),

wherein QC denotes the compression coefficient
QC=Δs/ΔP in the region of the measurement phase, said
compression coefficient resulting as the ratio of the change in pressure
ΔP for an associated traveled distance Δs of the piston in
question, and wherein ΔPtheor(t) denotes the profile of the
theoretical pressure difference which describes the thermal equilibration
process and results from the profile of the theoretical dependence
Ptheor(t) minus the value for the pressure PM at the time at
which the measurement phase starts.

[0012] According to one embodiment of the invention, the control device
can use the relationship

P theor ( t ) = P e ( P M - P e ) - t - t 3
τ , ##EQU00001##

with the parameters Pe and τ, as the analytical theoretical
dependence for the profile to be expected of the pressure Ptheor(t),
wherein Pe denotes the pressure after the end of the thermal
equilibration and τ denotes the time constant of the equilibration
process, and wherein PM denotes the pressure at the time t3 at
which the measurement phase starts.

[0013] The control device can carry out the measurement phase during the
compression phase and use the data recorded during the measurement phase
for determining at least one parameter of a measurement dependence
Pmess(t) in such a way that the measurement dependence Pmess(t)
approximates the recorded measurements in the best possible manner. The
control device can determine the parameters of the theoretical dependence
Ptheor(t) from the parameters of the measurement dependence
Pmess(t) thus determined.

[0014] If the control device carries out the measurement phase shortly in
time before the end of the compression phase, it can use the theoretical
dependence Ptheor(t) as the measurement dependence Pmess(t). In
this case, the parameters determined for the measurement dependence can
be used without conversion for the theoretical dependence Ptheor(t)
and thus directly to determine the correction dependence scorr(t).

[0015] According to another embodiment, the control device can carry out
the measurement phase during the decompression phase, preferably shortly
in time before the end of the decompression phase, and use the data
recorded during the measurement phase for determining the parameters of a
measurement dependence Pmess(t) in such a way that the measurement
dependence Pmess(t) approximates the recorded measurements in the
best possible manner. The control device can then determine the
parameters of the theoretical dependence Ptheor(t) from the
parameters of the measurement dependence Pmess(t). However, in this
case, a conversion is regularly necessary for this purpose, since in the
measurement phase the free volume is larger during the decompression than
the free volume prior to the start of the compensation phase.

with the parameters PeD and τD, as measurement dependence,
wherein PeD denotes the pressure after the end of the thermal
equilibration and τD denotes the time constant of the
equilibration process in the decompression phase, and wherein PMD
denotes the pressure at the time t21 at which the measurement phase
starts. The control device can determine the parameters of the correction
dependence scorr from the pressure values PMD and PeD or
the pressure difference ΔP=PeD-PMD and the time constant
τD.

[0017] In order to determine a conversion rule, during a time period in
which the flow to be delivered by the piston pump unit and the
composition of the medium to be delivered are substantially constant, the
control device can both determine the parameters of the measurement
dependence by way of a measurement in the compression phase and also
determine the parameters in the decompression phase. By comparing
parameters that correspond to one another, in each case a conversion
rule, preferably a conversion factor, can then be determined in order to
calculate the relevant parameter determined in the decompression phase
into a parameter of the correction dependence.

[0018] Since the pressure profile during the measurement phase depends on
the properties of the medium, in particular its compressibility, the
control device also has to be supplied with this information in order to
determine the correction dependence. To this end, during the compression
phase, the control unit can record at least two measurements for the
pressure in the volume of the first piston-cylinder unit at at least two
piston positions or a measurement for a pressure difference ΔP for
a traveled distance of the piston Δs, and determine therefrom a
value for the compressibility or a value for the compression coefficient
Qc=Δs/ΔP, wherein the two measurements or the region of
the pressure difference are selected such that they are in the region of
the system pressure.

[0019] However, a value for the compressibility or the compression
coefficient Qc for the medium to be delivered may also be known to
the control device, for example filed in a memory, or be supplied to said
control device by a superordinate unit.

[0020] The control device can then use the value determined by it for the
compressibility or the compression coefficient Qc to determine the
correction dependence.

[0021] According to a further embodiment, rather than keeping the piston
position constant during the measurement phase, the pressure in the
volume of the piston-cylinder unit in question is kept constant during
the measurement phase. To this end, the control device must comprise or
realize a pressure control loop. Instead of the time profile of the
pressure, in this embodiment, the time profile of the piston position is
detected, said profile being necessary in order to achieve a constant
pressure. The correction dependence scorr is determined from these
measurement data such that in the compensation phase pressure drops or
flow drops are compensated or at least drastically reduced.

[0022] Of course, in this variant, too, the control arrangement can
determine the correction dependence scorr(t) such that the flow
fluctuations caused by the compressibility of the medium are compensated
by an addition of the correction dependence scorr(t) and the piston
movement of the at least one of the at least two piston-cylinder units,
which piston movement would bring about the desired flow without taking
into account the thermal equilibration processes.

[0023] Here, too, in order to determine the correction dependence
scorr(t), the control arrangement uses a predetermined theoretical,
preferably analytical dependence scorr--theor(t) for the
time profile of the piston position or the piston speed and determines
one or more parameters of this dependence using the measurement data
recorded during the measurement phase.

[0024] Of course, in this variant, too, during the determination of the
correction dependence scorr(t), the control device can take into
account the thermal equilibration occurring in the time period from the
start of the measurement phase to the start of the compensation phase.

[0025] The control device then determines the correction dependence
scorr(t) for the piston movement s(t) using the relationship

scorr(t)=scorr--theor(t)-scorr--theor-
(t5),

wherein t5 denotes the time at which the compensation phase starts.

[0026] According to one embodiment, the control device can determine the
correction movement, necessary theoretically for compensating the thermal
effect, of the work piston scorr--theor(t) using the
relationship

s corr_theor ( t ) = ( s M - s e ) - t - t 3
τ , ##EQU00003##

with the functional parameters se and τ, wherein se denotes
the piston position after the end of the thermal equilibration and τ
denotes the time constant of the equilibration process, and wherein
sm denotes the piston position at the time t3 at which the
measurement phase starts.

[0027] In an alternative, in which the control device carries out the
measurement phase during the compression phase and uses the data recorded
during the measurement phase for determining at least one parameter of a
measurement dependence smess(t) in such a way that the measurement
dependence smess(t) approximates the recorded measurements in the
best possible manner, the control device can determine the parameters of
the theoretical dependence scorr--theor(t) from the
parameters of the measurement dependence smess(t).

[0028] In this case, the control device can carry out the measurement
phase shortly in time before the end of the compression phase and use the
theoretical dependence scorr--theor(t) as the measurement
dependence smess(t). Since, in this case, the measured values are
determined in a pressure range which is located in the region of the
system pressure, it is possible to dispense with conversion of the
determined parameters into corresponding parameters of the correction
dependence.

[0029] Even when the pressure is kept constant during the measurement
phase, the control device can in this case carry out the measurement
phase during the decompression phase, preferably shortly in time before
the end of the decompression phase, and use the data recorded during the
measurement phase for determining the parameters of a measurement
dependence smess(t) in such a way that the measurement dependence
smess(t) approximates the recorded measurements in the best possible
manner. The control device can then determine the parameters of the
theoretical dependence scorr--theor(t) or the parameters
of the correction dependence scorr(t) from the parameters of the
measurement dependence smess(t).

[0030] In this alternative, in which the pressure is kept constant, the
control device can use the relationship

with the parameters seD and τD, for the measurement
dependence smess(t) wherein seD denotes the pressure after the
end of the thermal equilibration and τD denotes the time
constant of the equilibration process, and wherein se denotes the
pressure at the time t21 at which the measurement phase starts.
Since, here, the parameters seD and τD were determined
during the decompression phase, they have to be converted into
corresponding parameters of the correction dependence scorr(t). In
this case, in particular the pressure difference
ΔsD=seD-sMD can be converted into the pressure
difference Δs=sM-se. The same applies for the time
constants τD and τ.

[0031] For this purpose, during a period in which the flow to be delivered
by the piston pump unit and the composition of the medium to be delivered
are substantially constant, the control device can both determine the
parameters of the measurement dependence by way of a measurement in the
compression phase and also determine the parameters in the decompression
phase and, by comparing parameters that correspond to one another,
determine in each case a conversion rule, preferably a conversion factor,
in order to convert the relevant parameter determined in the
decompression phase into a corresponding parameter of the correction
dependence. This applies in particular when the parameters during the
compression phase are determined here by performing a measurement in the
vicinity of the system pressure.

[0032] According to another embodiment, the time constant τ or the
time constant τD can be predetermined as a constant having a
theoretically or empirically determined value and preferably be stored in
the control device. The latter can then use the predetermined time
constant in the determination of further parameters, in particular the
particular final pressure Pe, se, PeD, seD. This has
the advantage that the measurement phase can then be selected to be
considerably shorter, since in the extreme case, only two measurements,
specifically at the start and at the end of the measurement phase, are
enough to determine this parameter. Since these measurement points are
relatively far apart in time, measurement errors and noise are included
to a lesser extent in the measurement result.

[0033] Since the measurement is carried out in each case with non-moving
medium and the compensation takes place in the compensation phase with
moving medium, in order to take this difference into account, the control
device can use, instead of the time constant τ, an (optionally
additionally) corrected, effective time constant τeff, wherein
the correction takes place such that the effective time constant
τeff decreases with an increasing flow rate, wherein the control
device determines the effective time constant τeff preferably in
accordance with the relationship

τ eff = τ ( 1 - k F l F l max )
, ##EQU00005##

wherein Fl denotes the current flow rate and Flmax denotes the
maximum possible flow rate, and wherein k denotes a constant factor
between 0 and 1, which is determined by experiments or by simulation for
the pump type in question.

BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which are incorporated herein and
constitute part of this specification, illustrate presently preferred
embodiments of the invention, and, together with the general description
given above and the detailed description given below, serve to explain
features of the invention (wherein like numerals represent like
elements).

[0035]FIG. 1 shows a schematic illustration of a serial double piston
pump according to the prior art;

[0036]FIG. 2 shows a schematic illustration of a parallel double piston
pump according to the prior art;

[0037]FIG. 3 shows a schematic illustration of a parallel double piston
pump according to the invention;

[0038]FIG. 4 shows diagrams for explaining the functioning of a first
embodiment of a control arrangement according to the invention;

[0039]FIG. 5 shows diagrams for explaining the functioning of a further
embodiment of a control arrangement according to the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

[0040] In HPLC pumps, the principle of the double piston pump has largely
become established. In this case, for each pump, use is made of two
pistons which can be moved either via a common drive, for example via a
camshaft, or via individual drives. The piston movements are executed
such that the sum of the flows delivered by the two pistons corresponds
to the desired overall flow. In this case, a distinction is made between
serial double piston pumps and parallel double piston pumps. The present
invention can be applied to both pump types. Therefore, in the following
text, both functional principles are briefly explained.

[0041] In gradient pumps, the mixing can already take place on the intake
side, i.e. on the low-pressure side. In this case, only a single double
piston pump is used to generate the gradient (LPG=low pressure gradient).
However, the mixing can also take place on the high-pressure side
(HPG=high pressure gradient) instead, wherein a separate double piston
pump is used in this case for each solvent. Serial or parallel double
piston pumps can be used both for LPG and for HPG.

[0042] The present application can be applied to all of these cases.
However, a prerequisite for the application is that the double piston
pumps have independent drives for each individual piston. In all of the
following considerations, a single double piston pump of this type is
always considered.

[0043] Both serial double piston pumps and parallel double piston pumps
operate cyclically, i.e. a movement sequence that is substantially always
the same repeats periodically, with the period duration being called the
cycle time in the following text. An example of a serial double piston
pump is found in EP 334 994 B1 or in U.S. Pat. No. 5,114,314 A.

[0044] The general functional principle of such serial double piston pumps
according to the prior art is explained briefly in the following text
with reference to FIG. 1.

[0045] The serial double piston pump 1 consists of a first piston-cylinder
unit or working pump 10 and a second piston-cylinder unit or compensation
pump 20. The working pump 10 consists of a working piston 12 which enters
a working head 11 and is sealed off by means of a seal 16. The drive 15
can move the working piston via an actuating element 14, wherein the
remaining free volume 13 in the working head depends on the particular
piston position. This free volume is connected to an inlet valve 17 and
an outlet valve 18 via connecting capillaries 19. In the simplest case,
these valves are passive return valves, for example ball valves, which
are arranged in FIG. 1 such that they allow only a throughflow from the
bottom to the top. If the working piston 12 is withdrawn, i.e. moved
toward the left in FIG. 1, the free volume 13 in the working head
increases in size, the inlet valve 17 opens and fresh solvent is drawn in
from a storage container (not illustrated) via the intake line 50. If the
working piston 12 is moved forward, i.e. toward the right in FIG. 1, the
free volume 13 decreases in size, the inlet valve 17 closes and the
outlet valve 18 opens. The displaced volume is delivered by the
connecting line 51 in the direction of the outlet.

[0046] The compensation pump 20 consists of a compensation head 21 having
the compensation piston 22, seal 26, actuating element 24 and drive 25.
While the working pump 10 is delivering solvent, the compensation piston
22 is withdrawn slowly so that the free volume 23 increases in size and a
part of the flow delivered by the working pump 10 is stored in the
compensation head 21. While the working pump 10 is drawing in new solvent
and thus does not deliver a flow, the compensation piston 22 is moved
back into the working head so that the volume 23 is continuously reduced
in size and the displaced solvent maintains the flow at the outlet 52.
The piston speeds are in this case selected such that the flow at the
outlet 52 corresponds at any time to the desired value.

[0047] An example of a parallel double piston pump can be found in U.S.
Pat. No. 4,137,011 A. The underlying principle of such parallel double
piston pumps is intended to be explained by way of the schematic
illustration in FIG. 2.

[0048] The parallel double piston pump 3 consists of two generally
identical working pumps 30 and 40 which are each constructed in the same
way as the working pump of the serial double piston pump. The components
31 to 39 and 41 to 49 correspond to the components 11 to 19 of the
working pump 10 and are numbered analogously thereto.

[0049] The two working pump pistons 30, 40 alternately deliver the desired
flow, i.e. while one working piston delivers the flow, the other draws in
new solvent and vice versa. Inlets and outlets of the two pumps are each
connected in parallel via the connecting capillaries 70 to 73 and the
T-pieces 76 and 77, so that the two working pumps can draw in new solvent
via a common intake line 75 and can make the delivered flow available at
a common outlet 74.

[0050] Both a serial double piston pump according to FIG. 1 and also a
parallel double piston pump according to FIG. 2 are capable, given
appropriate control of the piston movement, of delivering a continuous
flow that is largely free of pulsing at the outlet 52 and 74,
respectively. On account of the flow resistance of the chromatographic
separating column, a counter-pressure, which is also present at the pump
outlet 52 and 74, respectively, and is designated system pressure in the
following text, is produced in the medium to be delivered.

[0051] At higher operating pressures, the compressibility of the solvent
becomes increasingly noticeable. In the following text, the processes
which take place after a working pump has just drawn in new solvent are
considered. The working pump in question is designated first working pump
here, this meaning the (only) working pump in the case of a serial double
piston pump and, in the case of a parallel double piston pump, meaning
that working pump which has just drawn in new solvent at the time under
consideration. The compensation pump or second working pump is designated
other pump in the following text.

[0052] When the first working pump draws in new solvent, the solvent is
initially pressureless in the working head, i.e. in the free volume 13 or
33 or 43, while the other pump maintains the system pressure at the pump
outlet 52 and 74. Before the first working pump can deliver solvent in
the direction of the pump outlet, the solvent first has to be compressed
to the system pressure in order that the associated outlet valve 18 or 38
or 48 opens. This is known as compression and for this purpose the free
volume 13 or 33 or 43 has to be reduced in size. This takes place by the
first working piston 12 or 32 or 42 moving forward, with the travel that
is necessary for compression depending on the system pressure and on the
compressibility of the solvent in question. As soon as the compression is
complete and the system pressure has been reached in the first working
head, the associated outlet valve opens and the solvent displaced by the
further piston movement is delivered in the direction of the outlet. The
corresponding flow is added to the flow delivered by the other pump.
Therefore, at this moment the piston speeds have to be changed such that
an undesired change in the overall flow and thus also of the system
pressure is avoided. This moment is known as transfer, since in this case
the delivery of flow is transferred from the second pump to the first
working pump. Following the transfer, the piston of the other pump is
withdrawn in order to store or draw in solvent for the next stroke.

[0053] Depending on the construction of the pump, the transfer can take
place suddenly or gradually. Similarly, the time at which the transfer
starts can be determined in various ways. There are various known
technical solutions for this purpose. The present invention can be
applied to all of these solutions.

[0054] The transfer is followed by the delivery phase in which the working
pump in question delivers the flow.

[0055] During the compression phase, work is undertaken on the solvent,
since the piston in question has to negotiate a travel counter to the
pressure force. The compression work to be undertaken per pump cycle
increases approximately quadratically with the system pressure and leads
to heating of the solvent during the compression. On account of the
thermal expansion of the solvent, the pressure rises more quickly above
all in the upper pressure range than would actually be expected.

[0056] During the compression, the temperature of the working head 11 or
31 or 41 surrounding the solvent remains approximately constant, since
the latter has a relatively large thermal capacity and the solvent cannot
emit the compression heat as quickly as desired. As soon as the system
pressure has been reached in the working head and the transfer begins,
the pressure in the working head remains constant so that no further
energy is supplied to the solvent. Now, a thermal equilibration process
takes place, i.e. the solvent emits the compression heat as far as
possible to the working head. The time constant of this equilibration
process depends substantially on the thermal capacity and thermal
conductivity of the solvent and of the working head.

[0057] As a result of the cooling, the liquid volume is decreased. Since
the working pump is already involved in generating flow at this time,
this contraction in volume is at the expense of the flow delivered at the
outlet, i.e. the flow decreases for as long as the cooling process
continues. This is noticeable in the cyclical operation of the pump as
undesired periodic flow pulsing or pressure pulsing.

[0058] There are already a number of known approaches for reducing the
problem of pulsing caused by thermal effects.

[0059] For example, U.S. Pat. No. 5,108,264 A (column 6, lines 31 et seq.)
proposes calculating the thermal effect to be expected from the
compressibility and the system pressure and to compensate it by
corresponding piston movements, with a fixed time constant of 3 s being
assumed for cooling. Such a calculation is possible when the properties
of the solvent, in particular its specific thermal capacity and thermal
conductivity, are known precisely and are always the same. However, this
is not generally the case in HPLC pumps, which are intended to operate
with different solvents. The properties of all solvents to be used would
have to be determined in advance and stored in tables, this being
associated with corresponding effort. Therefore, this method can be used
only with major restrictions for universally usable HPLC pumps.

[0060] U.S. Pat. No. 5,108,264 A furthermore proposes (for example claim
4) measuring the system pressure prior to the transfer and controlling
the piston movement by means of a control loop such that no drop in
pressure occurs. A disadvantage with the use of such a pressure control
loop is its susceptibility to faults by way of external influences.
Specifically, drops or fluctuations in the system pressure can also be
brought about for example by the switching of switching valves in the
downstream further components of the chromatography system, by changes in
the flow resistance of the chromatography column or by parallel-connected
pumps in the case of an HPG pump. Such externally caused pressure
fluctuations can result in erroneous behavior of control pressure loops.
This could be avoided theoretically by using flow regulation instead of
pressure regulation. However, this is technically considerably more
difficult and more expensive to realize.

[0061] US 2008/0206067 A1 also deals with the same problems. Here, the use
of control pressure loops is likewise proposed and this would lead to the
above-described problem. As an alternative solution, it is proposed that
the compression already be carried out some time before the transfer is
due, so that the thermal effect has already abated. A disadvantage with
this solution is that the abatement of the thermal effect, as mentioned
in U.S. Pat. No. 5,108,264 A, lasts for about 3 seconds. However, in
conventional HPLC pumps, at higher flow rates, the entire cycle time is
only about one second. At least half of this is required for drawing in,
compression and delivery. The remaining time is much too short to allow
the thermal effects to abate sufficiently. Thus, the proposed method does
not provide a usable solution precisely for high flow rates at which the
drops in the flow are particularly critical on account of the usually
high pressures and high compression speeds.

[0062] US 2010/0040483 A1 proposes avoiding the entire problem by
separating the thermodynamic work of pressure generation from the precise
flow generation. However, two pumps connected in series are necessary for
this purpose, and this represents disadvantageously high complexity.

[0063] Similarly to in U.S. Pat. No. 5,108,264 A, WO 2006/103133 A1 also
proposes calculating the thermal effects to be expected from the
properties of the solvents in question and to compensate them by way of
corresponding piston movements.

[0064] Proceeding from this prior art, the invention is based on the
problem of creating a control arrangement for controlling a piston pump
unit for liquid chromatography, in particular high-performance liquid
chromatography, which makes it possible, in the case of a double piston
pump--or more generally, in the case of a multiple piston pump--to
substantially reduce or avoid the pulsing, brought about by the
compression work and the associated thermal effects, in the flow without
having to accept the disadvantages, explained above, of the known
approaches. In particular, the solution according to the invention is
intended to be adapted automatically to the properties of each particular
solvent, it is not intended to be disrupted by externally caused pressure
fluctuations and it is intended to function even at short cycle times.

[0065] The invention is based on the finding that the profile of the
thermal effect can be predicted on account of a measurement which is
carried out prior to the transfer, i.e. before the compensation phase in
which the thermal equilibration between the medium and the environment
occurs. On account of this predicted profile, it is possible to determine
which piston movement will be necessary for correction purposes after the
transfer.

[0066] The method according to the invention can be used to improve serial
or parallel double piston pumps (or multiple piston pumps which have more
than two piston-cylinder units) according to the prior art. A
prerequisite for the application is merely that each working pump has a
pressure measuring arrangement by way of which the pressure in the
working head can be determined. In this case, it is not important whether
the pressure is determined directly, i.e. with the aid of a pressure
sensor, or indirectly by way of the forces or deformations exerted by the
pressure.

[0067] The invention is described in the following text with reference to
the embodiment in FIG. 3, which corresponds substantially to the known
embodiment of a double piston pump 3, since the invention can be realized
purely by way of a special control of the drive taking into account
corresponding measurement signals or measurement and calculation results.
Mutually corresponding components in FIGS. 2 and 3 are therefore provided
with identical reference signs.

[0068] In a difference from FIG. 2, the double piston pump 3 has a control
device 5 which controls the drives 35 and 35 of the two working pumps 30,
40, using the method described below. Provided in each piston-cylinder
unit 31, 41 is a pressure sensor 7, the signal from which is supplied to
the control unit 5. In addition, a device for recording the position of
the pistons 32, 42 is provided and may be integrated into the respective
drive 35, 45. Of course, said device can also be arranged directly on the
piston-cylinder units 31, 41. The signals from these recording devices
are likewise supplied to the control unit 5.

[0069] It is also possible for just one of the pumps 30, 40 to be equipped
with corresponding sensors, in particular when the pumps are identical
pumps having the same behavior, since then the in each case other pump
can be controlled in a corresponding manner using the results obtained
for the pump having sensor devices.

[0070] If the invention is applied to a serial double piston pump
according to FIG. 1, then all that is necessary is for the working pump
10 to be provided with corresponding sensors.

[0071] The method according to the invention is explained in the following
text with reference to the embodiment illustrated in FIG. 3 of a parallel
double piston pump 3 by way of the diagrams illustrated in FIG. 4.

[0072] As can be seen from FIG. 4, the time axis is the same for all three
diagrams and shows a section of the pumping cycle, specifically the
compression phase, and also a certain period of time before and after.
The pump, which is currently carrying out the compression, is denoted
first working pump again, analogously to the above description. In the
case of the parallel double piston pump according to FIG. 3, the
processes shown take place alternately in the two working pumps 30, 40.
The control device 5 in this case takes over all the necessary functions
for controlling the drives 35, 45 and for recording and evaluating the
signals from the pressure sensors 7 and the sensors integrated in the
drives for recording the position of the pistons 32, 42.

[0073] The top diagram shows the profile of the pressure P(t) in the first
piston-cylinder unit or the first working head 31, 41 over the time axis,
wherein Psys represents the system pressure which is assumed in this
example to be constant.

[0074] The middle diagram shows the position sP of the first working
piston 32, 42 over the time axis, wherein in the zero position, the
piston is completely withdrawn, i.e. entirely on the left-hand side in
FIG. 3.

[0075] The bottom diagram shows the associated speed vP of the first
working piston 32, 42. For the sake of simplification, instead of the
real, ramp-like speed transitions, idealized, abrupt changes in speed are
illustrated.

[0076] At the start, i.e. prior to the time t1, the first working
pump 30, 40 draws in new solvent. The pressure corresponds here to the
ambient pressure. On account of the negative speed v1 of the first
working piston 32, 42 in this intake phase or filling phase, the piston
position changes in the zero direction. This is illustrated by the curved
section 110 of the middle diagram in FIG. 4. The zero point of the piston
position sP=0 corresponds to the rear reversal point of the piston
32, 42.

[0077] At the time t1, the piston reaches its rear reversal point and
now moves forward at the speed v2. The solvent located in the
working head is compressed, thereby leading to a pressure rise
corresponding to the curve section 101 in the middle diagram in FIG. 4.
This section up to the point at which the system pressure Psys is
reached is denoted the compression phase. As a result of the work
supplied during the compression, the medium to be delivered or the
solvent is heated.

[0078] During the compression, the compressibility of the solvent, i.e.
the relationship between the change in volume and the change in pressure,
is measured. To this end, in each case when a first measured pressure
PC and a second, higher measured pressure PM are reached, the
associated piston positions sC and sM are stored (times t2
and t3). The compressibility can be calculated from the measurements
(as described for example in U.S. Pat. No. 4,255,088 A). However, for the
purpose of simplification, it is sufficient to calculate a compression
quotient QC which expresses the relationship between the change in
distance and the change in pressure according to the following
relationship:

Q C = Δ s Δ P = s M - s C
P M - P C ( 1 ) ##EQU00006##

The measured pressures PM and PC are intended both to be
located in the region of the system pressure and have to be selected such
that, even in the case of inaccuracies in pressure recording, the actual
measured pressure in no way reaches the system pressure, and that the
differences in pressure and distance are sufficiently large in order to
determine QC precisely to a few percent.

[0079] When the second measured pressure PM is reached, i.e. shortly
before the system pressure Psys would be reached, the movement of
the working piston 12 or 32 or 42 and thus the compression continues to
be stopped (at the time t3). There then immediately follows a short
measurement phase or measurement interval 103. During the measurement
phase 103, the working piston is not moved further, i.e. the speed
v3 is zero in this phase.

[0080] During this measurement interval, no further energy is supplied to
the previously compressed solvent, and the available volume remains
constant. Since, on account of the compression heat, the solvent has a
higher temperature than the surrounding working head, a thermal
equilibration process starts, in which the solvent emits heat to the
working head 31, 41. The resulting volume contraction results in a
pressure drop 102 in the pressure profile, which is illustrated in the
top diagram in FIG. 4. This time profile of the pressure P(t) is recorded
by the control device 5 by means of the pressure sensors 7 thereof. To
this end, the pressure P(t) in the working head is measured a number of
times at time intervals during the duration of the measurement interval
103. This results in a measured pressure curve which reproduces the
profile of the pressure drop 102 as a function of time. In reality, the
sensors used for measurement exhibit a certain amount of noise. In order
nevertheless to record the pressure curve with sufficient accuracy, the
measurement interval therefore has to be selected to be sufficiently
long. Expediently, the duration of the measurement interval should be
between 0.1 s and 1 s, preferably at about 0.5 s.

[0081] If the piston 32, 42 were allowed to stand for a relatively long
time in the position sM, the thermal effect would gradually abate
and the pressure drop would slow in accordance with the curve 105 in the
top diagram in FIG. 4. This corresponds to the above-discussed solution
according to the prior art, which is not applicable on account of the
high time requirements at relatively high flow rates.

[0082] In the method according to the invention, in contrast to the prior
art, there is no waiting until the thermal effect has largely abated, but
rather the compression is continued at the time t4 (the end of the
measurement phase), until the system pressure Psys has been reached.
This process is known as residual compression and starts immediately
after the end of the short measurement interval 103, i.e. before the
thermal effect has abated.

[0083] During the residual compression, the pressure in the working head
rises in a manner corresponding to the curve 104 (see the top diagram in
FIG. 4) and reaches the system pressure at the time t5. At this time
t5, the relevant outlet valve 38, 48 opens and the transfer begins.
As is known from the prior art, the speeds of one or both pistons 32, 42
now have to be adapted in a compensation phase, which represents the
first part of the respective delivery phase of the pump, such that the
overall flow does not change in an undesired manner.

[0084] On account of the short measurement phase 103, at this time
t5, the thermal effect has abated only a little, i.e. the medium to
be delivered or solvent is still warmer than the surrounding working head
31, 41. The further temperature equilibration takes place during the
compensation phase (i.e. during the transfer and the following delivery
phase). The volume contraction resulting from the change in temperature
reduces the flow delivered at the outlet 74 of the entire double piston
pump 3. Without further measures, i.e. application of the movement
profile 117 or the speed 127 (middle and bottom diagram, respectively, in
FIG. 4), after the transfer has started, the flow delivered by the entire
double piston pump and thus also the system pressure Psys drop in an
undesired manner corresponding to the curve 107.

[0085] In order to avoid this, the volume contraction is calculated
according to the invention from the time profile of the measured pressure
curve 102 and compensated by a corresponding superposed piston movement
scorr(t).

[0086] In order to calculate the volume contraction, consideration is
given first of all to the conditions which would result if the piston
continued to remain stationary after the measurement phase 103, i.e.
starting at the time t4. In this case, the curve 102 would continue
and the pressure would thus follow the curve 105. This curve can be
extrapolated relatively easily from the measured pressure curve 102,
because the basic profile of such equilibration processes is known. To a
first approximation, the equilibration process proceeds according to the
following equation:

P theor ( t ) = P e + ( P M - P e ) - t -
t 3 τ ( 2 ) ##EQU00007##

In this case, Pe is the final pressure which would be reached
theoretically after the equilibration process has fully abated, PM
is the starting pressure at the time t3 and τ is the time
constant of the equilibration process (this can take for example about 3
s). This functional approach according to equation (2) is fit to the data
recorded in the measurement interval 103, i.e. the unknown parameters
Pe and τ are optimized, for example with the aid of the method
of least squares, such that the functional profile P(t) corresponds
optimally to the measured data.

[0087] The function determined in this way corresponds to the theoretical
pressure curve 105 which would result if the working piston continued to
be stationary even after the time t4.

[0088] If the thermal effect were not present, the pressure would already
remain constant at P=PM starting at the time t3. Consequently,
it is merely necessary to subtract PM from the right-hand part of
equation (2) in order to obtain the (negative) theoretical change in
pressure ΔPtheor(t) caused by the thermal effect:

The correction movement scorr--theor(t) of the working
piston, said correction movement scorr--theor(t)
theoretically corresponding to the profile of the change in pressure
ΔPtheor(t) in order to compensate the thermal effect, can be
calculated with the aid of the compression coefficient QC to be
determined according to equation (1):

Although the above calculations relate to the conditions with the outlet
valve 38, 48 closed, the volume contraction is independent of whether the
outlet valve is open or closed. Therefore, the calculated correction
movement can be applied even with the outlet valve 38, 48 open.

[0089] That part of the thermal effect which occurs before the start of
the transfer, i.e. where t<t5, is automatically compensated
during the residual compression, since the pressure of the working pump
is increased during the residual compression in any case up to the system
pressure Psys or until the outlet valve 38, 48 opens.

[0090] Accordingly, starting from the time t5, only the remaining
correction dependence scorr--theor(t) still has to be
carried out. For the correction dependence corrected in this way, the
relationship

scorr(t)=scorr--theor(t)-scorr--theor-
(t5) (5)

results, wherein the value scorr--theor(t5) is
subtracted from equation (4). This therefore results overall in the
following relationship for the correction dependence scorr(t):

The working piston 32, 42 in question is displaced, in addition to the
normal piston movement (curve 117 in the middle diagram in FIG. 4), by
the distance scorr(t) calculated in this manner, thereby resulting
in the curve 116. As a result, the free volume 33, 43 of the
piston-cylinder unit 31, 41 in question is smaller than would be the case
without correction, with the result that the volume contraction is
compensated. Expressed in speeds, instead of the normal piston speed 127,
first of all a higher piston speed as per curve 126 is traveled at, so
that an additional flow is delivered to compensate the thermal effect. As
a result, a pressure drop as per curve 107 is avoided and the pressure
follows curve 106 (cf. the bottom diagram in FIG. 4).

[0091] In principle, a different measurement dependence Pmess(t)
could be used in the above variant in order to adapt to the measurements
recorded in the measurement phase, and the parameters Pe and τ
of the theoretical correction dependence according to equation (4) or the
correction dependence according to equation (6) could be calculated from
said measurement dependence Pmess(t), in particular the functional
parameters thereof.

[0092] However, in the variant explained above, the theoretical dependence
Ptheor(t) according to equation (2) was used as the measurement
dependence Pmess(t).

[0093] By implementing this method in the control device 5, the drop in
flow or pressure, which would normally take place in the parallel double
piston pump 3 on account of the compression heat during and after the
transfer, can be completely compensated or at least drastically reduced.
Of course, the same also applies for the case, not explicitly explained,
of this procedure being used in a serial double piston pump according to
FIG. 1.

[0094] In any case, in all of these variants, after the compression phase
but before the start of the transfer, i.e. before the start of the
delivery phase (or of the compensation phase), a short measurement phase
is introduced in which the time pressure profile which results from the
starting thermal equilibration process of the compression heat is
measured, with the further, expected time profile of the volume
contraction or a correction movement of the piston being calculated from
this measured pressure profile, said correction movement being necessary
to compensate this volume contraction.

[0095] If the measurement phase is carried out in a region in which the
pressure corresponds approximately to the system pressure Psys, then
the influence of the residual compression and thus the influence of the
energy supplied in the latter can be ignored. However it is also possible
to carry out the measurement phase at a lower pressure (at which the
compressibility of the medium is already taking effect) and to convert
the parameters Pe and τ which are measured at the lower
pressures into the parameters which would result at pressure values in
the region of the system pressure Psys', taking into account a
theoretically or empirically determined rule.

[0096] However, it is possible in principle to obtain all the information
necessary for calculating the correction movements during the method by
way of measurements. Therefore, the method can be adapted automatically
to virtually any desired solvents. In contrast to known methods, in which
the correction is calculated from already known physical properties of
the solvents, in such a realization of the above-explained method, it is
not necessary to enter the type of solvent currently being used or to
determine or store the solvent properties separately. This is
particularly advantageous in gradient pumps according to the LPG
principle, in which the solvents are mixed at or upstream of the pump
inlet in a variable composition, such that the properties of the mixture
change depending on the respective mixing ratio. The method according to
the invention automatically determines the optimum correction movement
for the current mixing ratio. In some solutions according to the prior
art, the physical properties for each mixing ratio that occurs have to be
known, this requiring a very large amount of effort.

[0097] A further advantage of this method is that it operates
independently of changes in the system pressure. Even if a change in
system pressure takes place during the short measurement phase, this does
not disrupt the measurement since the relevant outlet valve is still
closed during the measurement. While the correction is being carried out,
changes in the system pressure likewise have no disruptive influence
since the correction takes place independently of the pressure, purely
volumetrically by way of piston movements calculated in advance. In
contrast thereto, pressure control loops, as are proposed in a number of
the known approaches, can be disruptively influenced by changes in the
system pressure, and this results in erroneous correction.

[0098] A further important advantage of the method is that it is
applicable even at high flow rates or short cycle times, since the
measurement process requires only a little time and the correction is
superposed on the normal piston movement without an additional time
requirement. It is not necessary to wait until the thermal effect has
largely abated, which would result in restrictions with regard to the
maximum flow rate.

[0099] Beyond the abovementioned specific advantages, the invention
provides the same advantages as the known solutions according to the
prior art: even at high working pressures and highly compressible
solvents, drops in flow or pressure, which are caused by the compression
heat being emitted to the pump head, are virtually completely eliminated.

[0100] In the following text, variants of the basic method are described,
the abovementioned advantages likewise applying to said variants.

[0101] In the above explanation, advantageously the measured pressure
PM at which the measurement phase 103 starts is selected to be the
same as the upper measured pressure for determining the compressibility
or the compression quotient QC. In other words: the measurement
phase for determining the correction dependence scorr(t) immediately
follows the phase of measuring the pressure values for determining the
compression quotient. Although this is expedient, it is not absolutely
necessary. The two measurements merely have to take place approximately
in the same pressure range. The compression quotient can, for example,
also be determined at somewhat lower pressures.

[0102] In principle, of course, the compression quotient or a value for
the compressibility can also be predetermined for the relevant medium to
be delivered, and be stored in the control device 5. However, this
variant loses the advantage that the method is adapted automatically to
the medium to be delivered.

[0103] In all of the variants discussed above and below, the correction
movement scorr(t) does not absolutely have to be carried out with
the relevant working piston, but rather the correction can be carried
out, in the case of a serial pump, also with the compensation piston 22
or, in the case of a parallel pump, also with the second working piston
32, 42, as long as the outlet valve thereof is open. It is likewise
possible to divide the correction movement between both pistons. In this
case, the sum of the correction movements has to be identical to the
determined correction movement scorr(t).

[0104] The simplest, and therefore preferred, embodiment is still,
however, carrying out the correction by way of the working piston which
has previously compressed the medium.

[0105] In a further variant of the method, a pressure control loop can
control the movement of the working piston during the measurement
interval 103 such that the pressure of the working pump remains constant
for the duration of the measurement interval. Then, rather than the time
profile of the pressure signal, the time profile of the relevant piston
position is recorded and evaluated as the measurement signal. Of course,
for this purpose, the control device necessarily has to be designed such
that the piston position can be recorded sufficiently precisely. However,
this does not necessarily mean that a separate arrangement has to be
provided for recording purposes. Since the piston positions and speeds
are predetermined by the same control arrangement, it may be quite
sufficient to use these default values. In many drive systems, it is then
possible to proceed from the assumption that the actual mechanical piston
position corresponds sufficiently accurately with the default value.

[0106] The procedure is similar to the above-described procedure. Since,
however, the piston position data recorded during the measurement
interval 103 directly represents the correction function here, the term
-QC is dispensed with in equation (4) and the correction dependence
scorr(t), for which the parameters se and τ are intended to
be determined, is:

wherein, in order to describe the correction movement theoretically
necessary to compensate the thermal effect, the relationship

s corr_theor ( t ) = ( s M - s e ) - t - t 3
τ ( 8 ) ##EQU00012##

was used here. The unknown parameters se and τ are determined
analogously to the already described procedure, using a measurement
function smess(t). In the simplest case, it is again possible to use
the relationship according to equation (7) as the measurement function
smess(t) when the measurement is carried out in the region of the
system pressure Psys. In this case, the following thus applies:

However, in principle, it is again also possible here to use some other
dependence as the measurement dependence and to determine the parameters
of the correction dependence according to equation (7) from the course
thereof or the functional parameters thereof.

[0107] In contrast to the pressure control loops proposed in the prior
art, here it is not the system pressure that is controlled but rather the
pressure of the working pump during the measurement interval. Since, at
this time, the associated outlet valve is still closed, the pressure
control loop is not influenced by any changes in the system pressure.

[0108] As described above, the measurement interval 103 (or the
corresponding measurement interval during the determination of the
profile of the piston position at a constantly controlled pressure) has
to have a certain minimum duration in order that the measured pressure
curve can be determined sufficiently precisely. The requirements placed
on the accuracy of the measurement can be greatly reduced if the time
constant τ is assumed to be fixed. Then, the only variable parameter
in the equations is the final pressure Pe or the final position
se. In order to determine these parameters, two measurement points
at the start and the end of the measurement interval are sufficient.
Since these two measurement points are located relatively far apart in
time, noise is included less strongly in the result of the calculation.
Conversely, in this way, a sufficiently precise result is still achieved
even in the case of a relatively short measurement interval. Such
shortening of the measurement interval is of interest when the cycle time
of the pump is short, i.e. above all at high flow rates.

[0109] Hitherto, in the above variants, the fact that the relevant working
piston 32, 42 delivers solvents located in the working head starting from
the transfer and is thus set into movement, has not been discussed. As a
result, the heat exchange between the medium and the surrounding
components is improved and so the solvent cools more rapidly than if it
is at a standstill. Thus, the volume contraction takes place more
quickly.

[0110] Therefore, the piston movement also has to be carried out more
quickly to compensate the thermal effect. This can be achieved according
to the invention in that the time constant τ of the compensation
movement is multiplied by a variable factor which becomes less with
increasing pump flow. At a low flow, i.e. when virtually no piston
movement takes place during the thermal effect, this factor is
approximately 1, i.e. the correction is carried out with the calculated
time constant. At a higher flow, the factor becomes smaller, and so the
time constant applied is shortened in a corresponding manner.

[0111] The function according to which the factor has to be calculated
depends on the geometry of the fluid components of the pump. However, in
practice, for example the following simple approach, in which the factor
decreases linearly with increasing flow, suffices:

τ eff = τ calc ( 1 - k Fl Fl max ) ( 10
) ##EQU00014##

In this case, τeff denotes the calculated time constant which is
used instead of τ in equation (6) and equation (7) for calculating
the correction movement. τcalc is the calculated time constant
which was determined by fitting the respective measurement dependence
Pmess(t) or smess(t) to the curve 102 (in the event that the
measurement dependence is selected to be the same as the theoretical
correction dependence Ptheor(t) or stheor(t)), k is a factor to
be defined between 0 and 1, Fl is the set flow in the double piston pump
in question, and Flmax is the maximum possible flow in the pump.

[0113] The factor k can be optimized easily by way of experiments for a
particular pump type. To this end, the pump is operated at high pressure
and medium to high flow and the value of k is varied such that an optimum
pulsing behavior results.

[0114] In the above-described embodiments, the thermal effect is recorded
in the measurement interval 103 preferably shortly before the transfer
which starts at the time t5. In this case, it is necessary always to
ensure that the transfer is ended in good time before the other pump has
reached the end of its delivery travel. If the set flow of the double
piston pump 3 increases during the measurement interval 103 or shortly
before the latter, the other pump reaches the end of its delivery travel
earlier than originally assumed and so the available measurement time is
suddenly greatly reduced.

[0115] This problem can be avoided by way of the alternative embodiment
described in the following text. This variant is based on the fact that,
in pumps of the type described, the free volume 13 or 33 or 43 (FIG. 1 or
2 and 3) in the relevant working head is also not 0 when the piston is in
its front end position, on account of unavoidable dead volumes. The free
residual volume that then remains is then under the system pressure
Psys at the end of the transfer. If the piston is then withdrawn in
order to draw in new solvent, this residual volume is initially
decompressed until the pressure in the working head reaches ambient
pressure and new solvent is drawn in.

[0116] During this decompression, a thermal effect likewise takes place
since the solvent cools on account of the expansion and the pressure
therefore reduces more quickly than would be expected on account of the
piston movement. This thermal effect proceeds inversely compared with
during the compression and can be recorded in an analogous way according
to the invention.

[0117]FIG. 5 shows, in a similar manner to FIG. 4, the pressure P, the
piston position sP and the speed vP of the working piston. At
the start, the working piston delivers solvent and reaches its front end
position at the time t20. Now, the piston is withdrawn at the speed
v21. As a result, more space is available to the remaining free
residual volume and the pressure rapidly drops. This process is known as
decompression in the following text.

[0118] The decompression is interrupted at the time t21 or when the
pressure PMD is reached, i.e. the piston is stopped (v20=0).
With that, the measurement interval 203 starts. In an analogous manner to
the above-described processes, a thermal equilibration process takes
place during the measurement interval, with the previously cooled solvent
being heated during said thermal equilibration process. This results in a
pressure rise as per curve 202, which is recorded by measurement.
Starting from the time t22, the remaining decompression is carried
out, i.e. the piston is withdrawn further. At the time t23, the
ambient pressure is reached, the inlet valve 17 or 37 or 47 is opened and
the drawing-in phase 110 starts, with new solvent being drawn in during
said phase 110. At the time t1, the piston reaches its rear end
position. This is followed by the compression 101, in which the piston
moves forward at the speed v2. At the end of the compression, i.e.
starting from the time t5, the compression heat is emitted, as
described above, resulting in a volume contraction which, without further
measures, would result in a pressure drop 107.

[0119] In this embodiment, the time profile of this volume contraction is
estimated from the data obtained during the measurement interval 203 and
is compensated in the same way as described above, in that, instead of
the piston movement 117, a corrected piston movement 116 is carried out.

[0120] Since, in this variant of the invention, the thermal effect is only
measured during the decompression and thus in the region of the front end
position of the piston, the effective liquid volume is much smaller than
the liquid volume at the end of the compression. Furthermore, the
majority of this liquid volume is located in a narrow region between the
piston and the pump head. Therefore, the thermal contact between the
liquid and the pump head is considerably better than when the piston is
located further toward the rear. As a result of both, the time constant
τD of this thermal equilibration process is considerably shorter
than the time constant τ which is effective in the compression phase
or toward the end of the compression phase. Therefore, a considerably
shorter measurement interval 203 is sufficient to record the
equilibration process than in the above-described method with measurement
at the end of the compression phase.

can thus be used as the measurement dependence, wherein τD
denotes the time constant of this exponentially proceeding measurement
dependence Pmess(t) PeD denotes the final pressure which would
be established at the end of the thermal equilibration (if the
measurement phase had been selected to be correspondingly long), and
PMD denotes the measured pressure at the start of the measurement
phase 203.

[0122] The conversion factor between the time constant τD
determined during the measurement interval 203 and the time constant
τ required for correction, and also between the pressure difference
ΔPD=PeD-PMD determined during the measurement
interval 203 and the pressure difference ΔP=Pe-PM
required for correction, can be determined empirically in a pilot test.
In this case, the measurement is carried out both during the
decompression in the measurement interval 203 and also at the end of the
compression in the measurement interval 103, and a conversion factor
between τ and τD or between ΔP and ΔPD is
determined. This pilot test can also take place in a fully automated
manner if no change in flow is currently to be expected.

[0123] However, in practice it is generally sufficient to use the
empirically determined values directly for both time constants τ and
τD without conversion and to calculate the corrected piston
movement 116 therefrom. This is because, in many cases, it will be
possible to assume that the time constants in normal operation are
identical to those during a pilot test. In other words, during normal
operation, the time constant τD determined during the pilot test
is used for measurement after the decompression, instead of determining
the time constant again from the measurements. Similarly, in order to
calculate the compensation movement, the time constant τ determined
during the pilot test is used directly without calculating this by
conversion of τD.

[0124] In order to create largely identical conditions during the
measurement in the decompression phase to those at the end of the
compression phase, it is favorable for the initial pressure of the
measurement PMD to be virtually identical to the ambient pressure
and for the decompression to be carried out as quickly as possible. In
this case, PMD must not be selected to be identical to the ambient
pressure, since otherwise already small inaccuracies of the pressure
sensors 7 could result in new solvent being drawn in prior to the
measurement. However, PMD can also be selected to be considerably
higher than ambient pressure, wherein, in this case, the measurement
result has to be converted in a manner corresponding to the lower
pressure difference.

[0125] This embodiment makes it possible to carry out the measurement in a
non-critical time interval and to manage with a shorter measurement
duration. If the pump flow delivered increases during the measurement,
the shortening of the overall time that is available can be reduced
without a problem by a higher drawing-in speed or more rapid compression.
Thus, in this case, the entire measurement duration that is required is
available.

[0126] Of course, it is also possible in this variant to constantly
control the pressure and to record the piston position as measurement
variable instead of keeping the piston position constant and recording
the pressure profile in the measurement phase.

[0127] Analogously to the above-explained embodiments, the relationship

can be used here as measurement dependence. The conversion factor between
the time constant τD determined during the decompression phase
and the time constant τ required for correction, and also between the
difference in distance Δs=seD-sMD determined during the
decompression phase and the difference in pressure
Δs=se-sm required for correction can be determined, as
described above, in a pilot test.

[0128] Finally, it should be noted that, of course, all of the
above-explained variants can be combined with one another, insofar as
this is sensible, and the variants are not mutually exclusive.